Question

select the correct answer.

mr. walter is remodeling his house and wants to design a rectangular garden in the backyard. the width of the garden, \\(w(a)\\), in feet, is modeled by this equation, where \\(a\\) is the area of the garden, in square feet.

\\w(a) = \sqrt{a} - 1.24\\

what is the average rate of change of the gardens width when the gardens area changes from 289 square feet to 400 square feet?

• the gardens width increases by approximately 18.76 feet for every 1-square-foot increase in the gardens area.
• the gardens width increases by approximately 15.76 feet for every 1-square-foot increase in the gardens area.
• the gardens width increases by approximately 0.27 foot for every 1-square-foot increase in the gardens area.
• the gardens width increases by approximately

Explanation:

Calculate the function values at the boundaries

$$
LATEXBLOCK0
$$

Compute the average rate of change

$$
LATEXBLOCK1
$$

Match with the given options

$$
LATEXBLOCK2
$$

Answer:

• The garden's width increases by approximately 18.76 feet for every 1-square-foot increase in the garden's area.
• The garden's width increases by approximately 15.76 feet for every 1-square-foot increase in the garden's area.
• The garden's width increases by approximately 0.27 foot for every 1-square-foot increase in the garden's area.
• The garden's width increases by approximately 0.03 foot (or 0.027 foot) for every 1-square-foot increase in the garden's area. (Correct answer)